Visiting the Viking Rib Stones

Visiting The Viking Rib Stones (Alberta)

Copyright: Dale Olausen 2023

The Viking Rib Stones are an interesting site from various points of view – ethnographic, archaeological, intercultural, indigenous, call it what you will.

I have visited this site on a number of occasions. It is a nice little half-day trip from Edmonton along some not-too-busy highways, culminating in a short drive through some pretty prairie secondary roads. This site is a little bit tricky to get to, as the province and the aboriginal groups want to maintain the site in a respectful way. However, there are directions available from a web search.

It’s worth the effort, especially if you have out-of-province visitors – I have found that our visitors to Alberta have always enjoyed the trip.

To begin with, I should note that the Viking Rib Stones have nothing to do with Vikings. They just happen to be located near the town of Viking, a community that was settled largely by Scandinavians early in the 20^th century.

They are, in fact, an excellent example of native art that is found in many areas of Alberta. Of course they are more than just art – they have significant cultural and spiritual significance for aboriginal people.

In strictly physical terms, they consist of two large rocks ( a large rock and a smaller rock), made of quartzite. They are solitary boulders that were carried to this spot by glaciers during the ice ages, and left behind as the glaciers retreated. The geological term for this is glacial erratic.

Upon this rock many markings have been carved. These carvings are meant to represent the ribs of two buffalo. The location is considered to be the dwelling place of the protector of the buffalo (known as Old Man Buffalo). There are also pits carved into the stones, representing holes left by arrows or bullets. These were not thought to harm the Old Man Buffalo, but rather to pass right through. There is also an interpretation that these pit represent the steady pounding of buffalo hoofs over the ages, rather in the manner that the steady drip of water will wear a pit into stone over time.

People, primarily aboriginal people one assumes, leave various objects of veneration and personal significance on and around the Rib Stones. Metals such as coins or spent bullets are common, as are jewellery and other personal items. But other items are also sometimes left, such as photos, books or tools, whatever might be significant to the leaver. Tobacco is also common, given its historical cultural significance to natives.

The Rib Stones site also has a nearly copse of trees, where aboriginal people have tied strips of cloth to these trees (known as prayer cloths), left as offerings to the spirits of the ancestors. The fencing around the little site might also used for this purpose.

The area surrounding the site, which has a small fence to enclose it, is left in a natural state, with grasses and wildflowers predominating.

A very large meteorite, known in English as the Iron Creek Meteorite, fell around here, at a location about 40 kilometers away, called Strawsack Hill. The configuration of the Rib Stones is thought to be aligned in such a way that it points to this location. It is also thought that some aspects of the meteorite are actually represented in the Rib Stones.

It is about half a meter in diameter, almost entirely composed of iron, and is considered to be a sacred object by the native population, the “father of meteorites”. It is thought to come from the gods or sky-people, a sort of visitor to the Earth, and therefore of great spiritual value. Native culture has a lot of tradition related to the sky and the stars, as might be expected given the big sky of the prairies and the dark nights of eras before electric lighting.

This meteorite rested on a high hill nearby, until the later 1800s when it was taken by missionaries and later claimed by researchers in various locations (including the University of Toronto). It was returned to Alberta in the early 1970s and has spent many decades at the Royal Alberta Museum, in Edmonton. There is a plan to return it to its original location, near this site, though the details are still being negotiated. According to the website of the Royal Alberta Museum there is a centre to be built at the site, so it will still be housed in a building. In that sense, it won’t really be returned to its ancestral state, but I suppose it would be too tempting a prize for all sorts of people if it was just dropped on the prairie.

Besides the Rib Stones, the site itself is very scenic, on a hill that commands a sweeping vista of the surround rolling prairie. There is a small parking lot, some signage, and the fenced in Rib Stones site (a low wooden fence, no gate, more to define the site than keep people out). It goes without saying that visitors should be respectful of the Rib Stones and the site in general.

After viewing the Rib Stones and associated area, one can stop in the nearby town of Viking, that has a homey little cafe and some other small-town tourist amenities (e.g. a Scandinavian "troll park", as Scandinavians have a thing for trolls, though the folklore type, not the internet type).

My dad (from Norway) homesteaded around here (the Iron Creek area) many decades ago, before going off to war and meeting his war bride, so I have a certain affinity for the area. On one trip to the area with my brother, the car window suddenly shattered. At first we thought someone might have been carelessly target shooting out in a field, but upon later reading I discovered that this isn’t that unusual an occurrence (lots of insurance claims are due to unexplained car window shattering). But it is nice to think that this might have been around the same spot as my dad’s homestead. You don’t have to be native to feel some sort of spiritual energy in the landscape.

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Now, if you like travel-related reading,why not try one of these:

On the Road with Bronco Billy

Spring is on us now, and that brings on thoughts of ROAD TRIP. Sure, it is still a bit early, but you can still start making plans for your next road trip with help of “On the Road with Bronco Billy”. Sit back and go on a ten day trucking trip in a big rig, through western North America, from Alberta to Texas, and back again. Explore the countryside, learn some trucking lingo, and observe the shifting cultural norms across this great continent. Then, come spring, try it out for yourself.

Amazon U.S.: http://www.amazon.com/gp/product/B00X2IRHSK

Amazon U.K.: http://www.amazon.co.uk/gp/product/B00X2IRHSK

Amazon Germany: http://www.amazon.de/gp/product/B00X2IRHSK

Amazon Canada: http://www.amazon.ca/gp/product/B00X2IRHSK

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A Drive Across Newfoundland

U.S.: https://www.amazon.com/dp/B07NMR9WM8

U.K.: https://www.amazon.co.uk/dp/B07NMR9WM8

Germany: https://www.amazon.de/dp/B07NMR9WM8

Japan: https://www.amazon.co.jp/dp/B07NMR9WM8

Canada: https://www.amazon.ca/dp/B07NMR9WM8

Australia: https://www.amazon.com.au/dp/B07NMR9WM8

India: https://www.amazon.in/dp/B07NMR9WM8

Newfoundland, Canada’s most easterly province, is a region that is both fascinating in its unique culture and amazing in its vistas of stark beauty. The weather is often wild, with coastal regions known for steep cliffs and crashing waves (though tranquil beaches exist too). The inland areas are primarily Precambrian shield, dominated by forests, rivers, rock formations, and abundant wildlife. The province also features some of the Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks of the Earth’s interior have been exposed at the surface, permitting one to explore an almost alien landscape, an opportunity available on only a few scattered regions of the planet.

The city of St. John’s is one of Canada’s most unique urban areas, with a population that maintains many old traditions and cultural aspects of the British Isles. That’s true of the rest of the province, as well, where the people are friendly and inclined to chat amiably with visitors. Plus, they talk with amusing accents and party hard, so what’s not to like?

This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.

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A Ride on the Kettle Valley Rail Trail: A Biking Journal Kindle Edition

by Dale Olausen (Author), Helena Puumala (Editor)

The Kettle Valley Rail Trail is one of the longest and most scenic biking and hiking trails in Canada. It covers a good stretch of the south-central interior of British Columbia, about 600 kilometers of scenic countryside. British Columbia is one of the most beautiful areas of Canada, which is itself a beautiful country, ideal for those who appreciate natural splendour and achievable adventure in the great outdoors.

The trail passes through a great variety of geographical and geological regions, from mountains to valleys, along scenic lakes and rivers, to dry near-desert condition grasslands. It often features towering canyons, spanned by a combination of high trestle bridges and long tunnels, as it passes through wild, unpopulated country. At other times, it remains quite low, in populated valleys, alongside spectacular water features such as beautiful Lake Okanagan, an area that is home to hundreds of vineyards, as well as other civilized comforts.

The trail is a nice test of one’s physical fitness, as well as one’s wits and adaptability, as much of it does travel through true wilderness. The views are spectacular, the wildlife is plentiful and the people are friendly. What more could one ask for?

What follows is a journal of two summers of adventure, biking most of the trail in the late 1990s. It is about 33,000 words in length (2 to 3 hours reading), and contains numerous photographs of the trail. There are also sections containing a brief history of the trail, geology, flora and fauna, and associated information.

After reading this account, you should have a good sense of whether the trail is right for you. If you do decide to ride the trail, it will be an experience you will never forget.

Amazon U.S.: https://www.amazon.com/dp/B01GBG8JE0

Amazon U.K.: https://www.amazon.co.uk/dp/B01GBG8JE0

Amazon Germany: https://www.amazon.de/dp/B01GBG8JE0

Amazon Canada: https://www.amazon.ca/dp/B01GBG8JE0

Amazon Australia: https://www.amazon.com.au/dp/B01GBG8JE0

Pi Day 2023 –Random PI

 

Pi Day 2023 –Random PI

Using Random Processes to Estimate PI

In the past I have done a few PI Day blogs using Monte Carlo process to estimate PI:

• Estimating Pi using normal distributons: https://dodecahedronbooks.blogspot.com/2020/03/pi-day-2020-pi-and-normal-distribution.html

• Estimating Pi by shooting arrows at a circle: https://dodecahedronbooks.blogspot.com/2019/03/pi-day-2019-shooting-arrows-at-target.html

• Estimating Pi with relatively prime numbers: https://dodecahedronbooks.blogspot.com/2018/03/pi-day-2018-prime-numbers-and-pi.html

• Estimating Pi with Buffon’s Needle: https://dodecahedronbooks.blogspot.com/2017/03/pi-day-floor-pie-and-floor-pi.html

A Monte Carlo simulation makes use of random numbers to simulate some process many, many times, then takes some sort of average result. For example, the shooting arrows Monte Carlo was performed as below:

• Create a random set of X and Y coordinates between -1 and +1.

• Calculate the Euclidean distance of each set of coordinates from the origin (i.e. use the Pythagorean Theorem of D=sqrt(X*X + Y*Y).

• Determine whether the point is within the unit circle (D<=1), or outside of the unit circle. Count the cases for each.

• Determine (in/(in + out)), multiply that by 4 and that’s your estimate of Pi. In other words, this will be the ratio of a unit circle that is inscribed in a unit square.

I have shown a visualization of one run of the simulation, using 1000 points. Yellow points are hits within the unit circle, red are misses outside the unit circle.

 

This process converges rather slowly (100 runs of 1 million points gives a value of Pi=3.14163 as compared to the accepted value of 3.14159), so it isn’t a great way to estimate Pi, but it is a good way to show that a random process can estimate Pi (technically it is a pseudo-random process, as the Excel random number generator is not technically random.

Is the Expansion of PI itself Random

A question that arises, is whether or not Pi itself is random. Well, at least it does to me. We all learn rather early in school that Pi is a number that never ends and never repeats itself – also known as an irrational number. Somewhat later in school we may learn that Pi is a transcendental number, which is defined as being the solution to a certain type of equation – quoting Wiki: “not the root of a non-zero polynomial of finite degree with rational coefficients”.

But is it therefore random? After all, if it goes on forever and never repeats itself, it seems intuitively obvious that it must be random. Alas, it isn’t that easy. Here are a few quotes from some books that I happen to have:

“presented with a number x in the unit interval, unless it is a very special kind like a finite or repeating decimal, nobody knows how to determine whether x is normal. Nobody knows, for example, whether the decimal part of the number pi is normal even though pi has been calculated to perhaps as many as a billion places.” (The Pleasures of Probability, Richard Isaac, p 119)

“At the moment, it is beyond mathematics to show that, for example, pi has a random decimal expansion...What we can do, however, is test a long, finite piece of the decimal expansion of Pi for statistical randomness. With pi, we have a number whose decimal expansion has been carried out to more terms than any other number, and as far as I am aware the sequence of the digits appears to be statistically random. So, although we cannot (at present) prove the decimal expansion Pi random we can get a certain degree of confidence that this is so from the statistical analysis of a long finite piece of this expansion.” (The Pleasures of Probability, Richard Isaac, p 148)

I should note that in this case, the term “normal” does not have anything to do with the Gaussian (or normal) distribution. In fact it actually refers to a uniform distribution – if all of the digits in the decimal expansion of Pi (0 to 9) were counted, and ratios produced, each digit should have one-tenth of the total, then it would be considered to be a “normal” number. In fact, that is one of the key indicators of a random sequence of numbers.

The other is a lack of “serial correlation”. That has nothing to do with breakfast, but rather is a way of saying digits shouldn’t follow each other in some sort of a pattern. For example 012345678900112233445566778899000111222333444555666777888999...is normal (each digit shows up one-tenth of the time) but not random as it does show serial correlation.

The one way to be sure that a number is actually random, is if we are sure that it has been generated by a random process. One example of a random physical process is radioactive decay – the sequence of numbers that can be generated by this process is random because the process itself is random. As I understand it, the randomness of radioactive decay is a result of quantum mechanics, which is inherently random due to the uncertainty principle. Some sort of chaotic process might also work, to produce a truly random sequence of numbers.

There is one escape hatch from this, at least to an extent, as is noted below:

“Digits in the decimal representations of approximations to transcendental numbers, such as Pi or e, or simpler irrational numbers , such as root-two, have often been suggested as streams of independent discrete uniform numbers...Most statistical streams from Pi and e (usually in base 10) have not detected nonzero correlations or departures from uniformity.” (Random Number Generation and Monte Carlo Methods, James E. Gentle, page 43-44)

“A sequence of digits could be called statistically random if it passes a battery of statistical tests for randomness. This kind of randomness ignores how the digits are actually generated; it only requires sequences of them to pass the statistical tests. The concept of statistical randomness is of the greatest importance for computers, It allows computer -generated deterministic sequences to substitute for actual random sequences because the deterministic sequences are statistically random. Statistical randomness is a much more useful idea than just plain randomness – it substitutes the extremely appealing and practical guide of statistical testing for the usually impossible task of determining how the digits were generated. It is operational in nature: if it acts random then it might as well be random.” (The Pleasures of Probability, Richard Isaac, p 147)

I should note that there are a large number of tests that are used for checking the randomness of a string of numbers (or other symbols that you could map to numbers). The generally fall into two categories:

• Goodness of fit tests (does the actual distribution of digits conform to the expected distribution?)

• Serial correlation tests (do the runs of repeating numbers found match what would be expected from a random sequence?)

There are many variations of tests. The idea is to run the sequence against a battery of tests. If it passes them all, then it gets the all-clear. If it passes most, then it might still be accepted (a judgment call). These tests are especially important for determining the reliability of random number generators in computer packages, such as Excel, SPSS, Matlab, etc..

It has long been said that a team of monkeys bashing away on typewriters would eventually produce Hamlet. So, does that prove that the monkey bashing is not random, as defined above?

Suppose that the monkeys typed random garbage for 10 to the 50^th power centuries, then Hamlet, then endless garbage again. Would the production of Hamlet prove that this was a non-random process? I think most people would say: “sort of, but not really”.

Coming back to Pi, Carl Sagan’s book “Contact” had a message from an alien species buried deeply in the expansion of Pi (base 11 or something like that). Would that actually be good evidence that the aliens exist, or is it just a weird fluke that you would eventually stumble upon in the far reaches of your way to infinity?

In theory I would say that it doesn’t prove their existence (we don’t know that Pi is actually a normal number) but in practice I would say that it does.

Sources:

Beckmann, Petr. A History of Pi (p. 101). St. Martin's Press. Kindle Edition.

The Pleasures of Probability, Richard Isaac, Springer.

Random Number Generation and Monte Carlo Methods, James E. Gentle, Springer, 2^nd Edition.

So, now that you have dutifully read some Pi Day math, you should read a science fiction book, or even better, a whole series. Book 1 of the Witches’ Stones series even includes a reference to pi.:

Kati of Terra

How about trying Kati of Terra, the 3-novel story of a feisty young Earth woman, making her way in that big, bad, beautiful universe out there.

http://www.amazon.com/gp/product/B00811WVXO

http://www.amazon.co.uk/gp/product/B00811WVXO

The Witches’ Stones

Or, you might prefer, the trilogy of the Witches’ Stones (they’re psychic aliens, not actual witches), which follows the interactions of a future Earth confederation, an opposing galactic power, and the Witches of Kordea. It features Sarah Mackenzie, another feisty young Earth woman).

https://www.amazon.com/dp/B008PNIRP4

https://www.amazon.co.uk/dp/B008PNIRP4

The Magnetic Anomaly: A Science Fiction Story

“A geophysical crew went into the Canadian north. There were some regrettable accidents among a few ex-military who had become geophysical contractors after their service in the forces. A young man and young woman went temporarily mad from the stress of seeing that. They imagined things, terrible things. But both are known to have vivid imaginations; we have childhood records to verify that. It was all very sad. That’s the official story.”

A short story of about 6000 works.

https://www.amazon.com/dp/B0176H22B4

https://www.amazon.co.uk/dp/B0176H22B4

The Zoo Hypothesis or The News of the World: A Science Fiction Story

In the field known as Astrobiology, there is a research program called SETI, The Search for Extraterrestrial Intelligence. At the heart of SETI, there is a mystery known as The Great Silence, or The Fermi Paradox, named after the famous physicist Enrico Fermi. Essentially, he asked “If they exist, where are they?”.

Some quite cogent arguments maintain that if there was extraterrestrial intelligence, they should have visited the Earth by now. This story, a bit tongue in cheek, gives a fictional account of one explanation for The Great Silence, known as The Zoo Hypothesis. Are we a protected species, in a Cosmic Zoo? If so, how did this come about? Read on, for one possible solution to The Fermi Paradox.

The short story is about 6300 words, or about half an hour at typical reading speeds.

https://www.amazon.com/dp/B076RR1PGD

https://www.amazon.co.uk/dp/B076RR1PGD